Computed Tomography (CT) is an imaging technology that uses computer-processed X-ray beams to produce tomographic images of specific areas of a scanned object. Each X-ray beam comprises bundles of energy (or “photons”) which, depending on the structure of the imaged material, may pass through, be absorbed by, or be redirected (i.e., scattered) by the structure. The degree to which an X-ray beam is reduced by an object during imaging is referred to as attenuation.
CT reconstruction is a computationally intensive process because the measurement operator does not possess a fast FFT-based implementation. Additionally, when reducing the radiation dose induced to the patient, one must rely on iterative reconstruction to model non-Gaussian noise and prior image knowledge, which further increases the cost.
To reduce the computational burden, iterative reconstruction methods for CT avoid considering all the measurements at each iteration. Conventional reconstruction methods include the Algebraic Reconstruction Technique for Gaussian noise and Ordered Subset EM for non-Gaussian noise. In Ordered Subset methods, the measurements are partitioned into several subsets, and at each iteration, the reconstruction is updated based on the measurements of one subset only. One can also regrid the sinogram to approach the measurement operator by an operator with parallel X-rays, which can be computed with a non-uniform Fast Fourier Transform, but this approximation can add artifacts to the reconstruction.